Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(60.6863055362\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.76156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.76156 | −1.59439 | −0.797193 | − | 0.603725i | \(-0.793683\pi\) | ||||
−0.797193 | + | 0.603725i | \(0.793683\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.761557 | 0.287842 | 0.143921 | − | 0.989589i | \(-0.454029\pi\) | ||||
0.143921 | + | 0.989589i | \(0.454029\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.62620 | 1.54207 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.864641 | 0.260699 | 0.130350 | − | 0.991468i | \(-0.458390\pi\) | ||||
0.130350 | + | 0.991468i | \(0.458390\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.62620 | 1.56043 | 0.780213 | − | 0.625514i | \(-0.215111\pi\) | ||||
0.780213 | + | 0.625514i | \(0.215111\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.62620 | −0.879482 | −0.439741 | − | 0.898125i | \(-0.644930\pi\) | ||||
−0.439741 | + | 0.898125i | \(0.644930\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.10308 | −0.458930 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.01395 | 1.67102 | 0.835512 | − | 0.549472i | \(-0.185171\pi\) | ||||
0.835512 | + | 0.549472i | \(0.185171\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.49084 | −0.864262 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.35548 | −1.36588 | −0.682939 | − | 0.730475i | \(-0.739299\pi\) | ||||
−0.682939 | + | 0.730475i | \(0.739299\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.11704 | −1.45786 | −0.728931 | − | 0.684587i | \(-0.759983\pi\) | ||||
−0.728931 | + | 0.684587i | \(0.759983\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.38776 | −0.415655 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.476886 | 0.0783995 | 0.0391998 | − | 0.999231i | \(-0.487519\pi\) | ||||
0.0391998 | + | 0.999231i | \(0.487519\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.5371 | −2.48792 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.65847 | −0.415184 | −0.207592 | − | 0.978216i | \(-0.566563\pi\) | ||||
−0.207592 | + | 0.978216i | \(0.566563\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.86464 | −1.04685 | −0.523424 | − | 0.852072i | \(-0.675346\pi\) | ||||
−0.523424 | + | 0.852072i | \(0.675346\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.25240 | −0.182681 | −0.0913404 | − | 0.995820i | \(-0.529115\pi\) | ||||
−0.0913404 | + | 0.995820i | \(0.529115\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.42003 | −0.917147 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.0140 | 1.40223 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.37380 | 0.326067 | 0.163033 | − | 0.986621i | \(-0.447872\pi\) | ||||
0.163033 | + | 0.986621i | \(0.447872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.76156 | 0.365777 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.49084 | −0.584657 | −0.292329 | − | 0.956318i | \(-0.594430\pi\) | ||||
−0.292329 | + | 0.956318i | \(0.594430\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8646 | −1.39107 | −0.695537 | − | 0.718490i | \(-0.744834\pi\) | ||||
−0.695537 | + | 0.718490i | \(0.744834\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.52311 | 0.443871 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.03228 | −0.126113 | −0.0630563 | − | 0.998010i | \(-0.520085\pi\) | ||||
−0.0630563 | + | 0.998010i | \(0.520085\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −22.1310 | −2.66426 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1816 | 1.20833 | 0.604166 | − | 0.796858i | \(-0.293506\pi\) | ||||
0.604166 | + | 0.796858i | \(0.293506\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.4017 | 1.91967 | 0.959837 | − | 0.280557i | \(-0.0905191\pi\) | ||||
0.959837 | + | 0.280557i | \(0.0905191\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.658473 | 0.0750400 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5693 | 1.41416 | 0.707081 | − | 0.707133i | \(-0.250012\pi\) | ||||
0.707081 | + | 0.707133i | \(0.250012\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.47689 | −0.164098 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.270718 | 0.0297152 | 0.0148576 | − | 0.999890i | \(-0.495271\pi\) | ||||
0.0148576 | + | 0.999890i | \(0.495271\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 20.3126 | 2.17774 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.387755 | 0.0411020 | 0.0205510 | − | 0.999789i | \(-0.493458\pi\) | ||||
0.0205510 | + | 0.999789i | \(0.493458\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.28467 | 0.449156 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.4157 | 2.32440 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.50479 | −0.863531 | −0.431765 | − | 0.901986i | \(-0.642109\pi\) | ||||
−0.431765 | + | 0.901986i | \(0.642109\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.4157 | 1.63342 | 0.816710 | − | 0.577049i | \(-0.195796\pi\) | ||||
0.816710 | + | 0.577049i | \(0.195796\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.64015 | 0.949872 | 0.474936 | − | 0.880020i | \(-0.342471\pi\) | ||||
0.474936 | + | 0.880020i | \(0.342471\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.28467 | −0.414215 | −0.207107 | − | 0.978318i | \(-0.566405\pi\) | ||||
−0.207107 | + | 0.978318i | \(0.566405\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.4200 | −1.28541 | −0.642703 | − | 0.766116i | \(-0.722187\pi\) | ||||
−0.642703 | + | 0.766116i | \(0.722187\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.31695 | −0.124999 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.3232 | −0.971125 | −0.485563 | − | 0.874202i | \(-0.661385\pi\) | ||||
−0.485563 | + | 0.874202i | \(0.661385\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 26.0279 | 2.40628 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.76156 | −0.253152 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2524 | −0.932036 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.34153 | 0.661963 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9817 | −1.50688 | −0.753440 | − | 0.657517i | \(-0.771607\pi\) | ||||
−0.753440 | + | 0.657517i | \(0.771607\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.9571 | 1.66908 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.541436 | −0.0473055 | −0.0236528 | − | 0.999720i | \(-0.507530\pi\) | ||||
−0.0236528 | + | 0.999720i | \(0.507530\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.761557 | −0.0660354 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.87859 | 0.245935 | 0.122967 | − | 0.992411i | \(-0.460759\pi\) | ||||
0.122967 | + | 0.992411i | \(0.460759\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.58767 | −0.304302 | −0.152151 | − | 0.988357i | \(-0.548620\pi\) | ||||
−0.152151 | + | 0.988357i | \(0.548620\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.45856 | 0.291264 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.86464 | 0.406802 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.7293 | 1.46229 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.8401 | −1.37959 | −0.689796 | − | 0.724004i | \(-0.742300\pi\) | ||||
−0.689796 | + | 0.724004i | \(0.742300\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.9817 | 1.38195 | 0.690975 | − | 0.722879i | \(-0.257182\pi\) | ||||
0.690975 | + | 0.722879i | \(0.257182\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.7755 | −1.35622 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8401 | 1.18437 | 0.592183 | − | 0.805804i | \(-0.298266\pi\) | ||||
0.592183 | + | 0.805804i | \(0.298266\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.55539 | −0.519876 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.10308 | 0.480990 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.3694 | −1.04717 | −0.523587 | − | 0.851972i | \(-0.675407\pi\) | ||||
−0.523587 | + | 0.851972i | \(0.675407\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.84632 | −0.761931 | −0.380966 | − | 0.924589i | \(-0.624408\pi\) | ||||
−0.380966 | + | 0.924589i | \(0.624408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.6541 | 1.43493 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.62620 | −0.353774 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.98168 | 0.226693 | 0.113346 | − | 0.993556i | \(-0.463843\pi\) | ||||
0.113346 | + | 0.993556i | \(0.463843\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.4017 | 0.932169 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.7938 | −0.881512 | −0.440756 | − | 0.897627i | \(-0.645290\pi\) | ||||
−0.440756 | + | 0.897627i | \(0.645290\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5693 | 1.08293 | 0.541465 | − | 0.840723i | \(-0.317870\pi\) | ||||
0.541465 | + | 0.840723i | \(0.317870\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30.0033 | 2.21791 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.13536 | −0.229280 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.42003 | −0.248771 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.2384 | −0.957900 | −0.478950 | − | 0.877842i | \(-0.658983\pi\) | ||||
−0.478950 | + | 0.877842i | \(0.658983\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.54144 | 0.182937 | 0.0914683 | − | 0.995808i | \(-0.470844\pi\) | ||||
0.0914683 | + | 0.995808i | \(0.470844\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.9109 | −1.41859 | −0.709295 | − | 0.704911i | \(-0.750987\pi\) | ||||
−0.709295 | + | 0.704911i | \(0.750987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.3126 | 1.43992 | 0.719960 | − | 0.694015i | \(-0.244160\pi\) | ||||
0.719960 | + | 0.694015i | \(0.244160\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.85069 | 0.201072 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.60162 | −0.393157 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 37.0741 | 2.57683 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.864641 | −0.0598085 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.0419 | −1.24205 | −0.621026 | − | 0.783790i | \(-0.713284\pi\) | ||||
−0.621026 | + | 0.783790i | \(0.713284\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −28.1170 | −1.92655 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.18159 | −0.419634 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −45.2943 | −3.06070 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.4017 | −1.37237 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.5231 | 0.905575 | 0.452787 | − | 0.891619i | \(-0.350430\pi\) | ||||
0.452787 | + | 0.891619i | \(0.350430\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.6016 | −0.902771 | −0.451386 | − | 0.892329i | \(-0.649070\pi\) | ||||
−0.451386 | + | 0.892329i | \(0.649070\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.5877 | 0.897898 | 0.448949 | − | 0.893557i | \(-0.351798\pi\) | ||||
0.448949 | + | 0.893557i | \(0.351798\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.81841 | −0.119643 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.5510 | 1.67390 | 0.836952 | − | 0.547277i | \(-0.184336\pi\) | ||||
0.836952 | + | 0.547277i | \(0.184336\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −34.7110 | −2.25472 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3309 | 0.732935 | 0.366468 | − | 0.930431i | \(-0.380567\pi\) | ||||
0.366468 | + | 0.930431i | \(0.380567\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.25240 | −0.0806739 | −0.0403370 | − | 0.999186i | \(-0.512843\pi\) | ||||
−0.0403370 | + | 0.999186i | \(0.512843\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.5510 | 1.12590 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.62620 | −0.357986 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.747604 | −0.0473775 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5939 | −0.668682 | −0.334341 | − | 0.942452i | \(-0.608514\pi\) | ||||
−0.334341 | + | 0.942452i | \(0.608514\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.92919 | 0.435635 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.153681 | −0.00958637 | −0.00479319 | − | 0.999989i | \(-0.501526\pi\) | ||||
−0.00479319 | + | 0.999989i | \(0.501526\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.363176 | 0.0225666 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −34.0279 | −2.10627 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.504792 | −0.0311268 | −0.0155634 | − | 0.999879i | \(-0.504954\pi\) | ||||
−0.0155634 | + | 0.999879i | \(0.504954\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.07081 | −0.0655324 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.49521 | −0.213107 | −0.106553 | − | 0.994307i | \(-0.533981\pi\) | ||||
−0.106553 | + | 0.994307i | \(0.533981\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.47252 | −0.332432 | −0.166216 | − | 0.986089i | \(-0.553155\pi\) | ||||
−0.166216 | + | 0.986089i | \(0.553155\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.8324 | −0.716127 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.9538 | 0.778317 | 0.389158 | − | 0.921171i | \(-0.372766\pi\) | ||||
0.389158 | + | 0.921171i | \(0.372766\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −37.5510 | −2.24812 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.153681 | 0.00916785 | 0.00458393 | − | 0.999989i | \(-0.498541\pi\) | ||||
0.00458393 | + | 0.999989i | \(0.498541\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.2341 | 1.08390 | 0.541952 | − | 0.840410i | \(-0.317686\pi\) | ||||
0.541952 | + | 0.840410i | \(0.317686\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.02458 | −0.119507 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.85069 | −0.226511 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.4865 | 1.37680 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.03853 | 0.119092 | 0.0595462 | − | 0.998226i | \(-0.481035\pi\) | ||||
0.0595462 | + | 0.998226i | \(0.481035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.88296 | −0.225312 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 45.0881 | 2.60751 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.22782 | −0.301326 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −45.3328 | −2.60430 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.5414 | −0.944070 | −0.472035 | − | 0.881580i | \(-0.656480\pi\) | ||||
−0.472035 | + | 0.881580i | \(0.656480\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −26.6218 | −1.51446 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.4725 | 1.21759 | 0.608797 | − | 0.793326i | \(-0.291652\pi\) | ||||
0.608797 | + | 0.793326i | \(0.291652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.12141 | −0.0633856 | −0.0316928 | − | 0.999498i | \(-0.510090\pi\) | ||||
−0.0316928 | + | 0.999498i | \(0.510090\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.8882 | −1.67869 | −0.839344 | − | 0.543601i | \(-0.817060\pi\) | ||||
−0.839344 | + | 0.543601i | \(0.817060\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.35985 | −0.356083 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.8324 | 0.660418 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.62620 | 0.201767 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 37.0602 | 2.04943 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.953771 | −0.0525831 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.3126 | −1.77606 | −0.888030 | − | 0.459786i | \(-0.847926\pi\) | ||||
−0.888030 | + | 0.459786i | \(0.847926\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.20617 | 0.120897 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.3511 | 1.43544 | 0.717718 | − | 0.696334i | \(-0.245187\pi\) | ||||
0.717718 | + | 0.696334i | \(0.245187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 28.5081 | 1.54835 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.01832 | −0.380063 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.2201 | −0.551835 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.77551 | 0.148997 | 0.0744986 | − | 0.997221i | \(-0.476264\pi\) | ||||
0.0744986 | + | 0.997221i | \(0.476264\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5510 | 0.618312 | 0.309156 | − | 0.951011i | \(-0.399953\pi\) | ||||
0.309156 | + | 0.951011i | \(0.399953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.2663 | −1.34862 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.40171 | −0.447178 | −0.223589 | − | 0.974684i | \(-0.571777\pi\) | ||||
−0.223589 | + | 0.974684i | \(0.571777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.62620 | 0.403621 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.7895 | −1.20278 | −0.601391 | − | 0.798955i | \(-0.705387\pi\) | ||||
−0.601391 | + | 0.798955i | \(0.705387\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.3126 | 1.48602 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.06455 | −0.212168 | −0.106084 | − | 0.994357i | \(-0.533831\pi\) | ||||
−0.106084 | + | 0.994357i | \(0.533831\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.2986 | −0.640241 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.80779 | 0.0938556 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.4017 | −0.952804 | −0.476402 | − | 0.879227i | \(-0.658059\pi\) | ||||
−0.476402 | + | 0.879227i | \(0.658059\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −41.3834 | −2.13135 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.23844 | −0.0636145 | −0.0318073 | − | 0.999494i | \(-0.510126\pi\) | ||||
−0.0318073 | + | 0.999494i | \(0.510126\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 46.8959 | 2.40255 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.8646 | −0.861743 | −0.430871 | − | 0.902413i | \(-0.641794\pi\) | ||||
−0.430871 | + | 0.902413i | \(0.641794\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −31.7572 | −1.61431 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.59392 | 0.435729 | 0.217865 | − | 0.975979i | \(-0.430091\pi\) | ||||
0.217865 | + | 0.975979i | \(0.430091\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.0602 | −1.46964 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.49521 | 0.0754233 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.0558 | 0.805818 | 0.402909 | − | 0.915240i | \(-0.367999\pi\) | ||||
0.402909 | + | 0.915240i | \(0.367999\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.10308 | 0.105286 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.8925 | −0.743698 | −0.371849 | − | 0.928293i | \(-0.621276\pi\) | ||||
−0.371849 | + | 0.928293i | \(0.621276\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −45.6681 | −2.27489 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.412335 | 0.0204387 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.3511 | −0.907404 | −0.453702 | − | 0.891153i | \(-0.649897\pi\) | ||||
−0.453702 | + | 0.891153i | \(0.649897\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.94940 | −0.392115 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.42003 | −0.168289 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.90754 | 0.485174 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.7509 | −1.69769 | −0.848847 | − | 0.528639i | \(-0.822703\pi\) | ||||
−0.848847 | + | 0.528639i | \(0.822703\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.1589 | −1.95722 | −0.978612 | − | 0.205713i | \(-0.934049\pi\) | ||||
−0.978612 | + | 0.205713i | \(0.934049\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.79383 | −0.281706 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.27405 | −0.400409 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.4340 | −0.648599 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.9571 | −1.68382 | −0.841912 | − | 0.539615i | \(-0.818570\pi\) | ||||
−0.841912 | + | 0.539615i | \(0.818570\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.13536 | 0.0545619 | 0.0272809 | − | 0.999628i | \(-0.491315\pi\) | ||||
0.0272809 | + | 0.999628i | \(0.491315\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.01395 | −0.383359 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.80009 | 0.324551 | 0.162275 | − | 0.986746i | \(-0.448117\pi\) | ||||
0.162275 | + | 0.986746i | \(0.448117\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.7003 | −1.41430 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −38.0679 | −1.80866 | −0.904330 | − | 0.426835i | \(-0.859629\pi\) | ||||
−0.904330 | + | 0.426835i | \(0.859629\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 46.5048 | 2.19960 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.5414 | −0.875024 | −0.437512 | − | 0.899212i | \(-0.644140\pi\) | ||||
−0.437512 | + | 0.899212i | \(0.644140\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.29862 | −0.108238 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −46.8959 | −2.20336 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.3738 | 0.765934 | 0.382967 | − | 0.923762i | \(-0.374902\pi\) | ||||
0.382967 | + | 0.923762i | \(0.374902\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.2847 | 0.760103 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.70470 | 0.0793959 | 0.0396979 | − | 0.999212i | \(-0.487360\pi\) | ||||
0.0396979 | + | 0.999212i | \(0.487360\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.0279 | 0.466036 | 0.233018 | − | 0.972472i | \(-0.425140\pi\) | ||||
0.233018 | + | 0.972472i | \(0.425140\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.7509 | −1.51553 | −0.757766 | − | 0.652526i | \(-0.773709\pi\) | ||||
−0.757766 | + | 0.652526i | \(0.773709\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.786137 | −0.0363004 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −40.9817 | −1.88834 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.93545 | −0.272912 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.9817 | 0.502816 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.2803 | −1.24647 | −0.623234 | − | 0.782035i | \(-0.714182\pi\) | ||||
−0.623234 | + | 0.782035i | \(0.714182\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.68305 | 0.122337 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.8540 | −0.766884 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0741 | 0.501817 | 0.250908 | − | 0.968011i | \(-0.419271\pi\) | ||||
0.250908 | + | 0.968011i | \(0.419271\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.9205 | 1.66960 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.11704 | −0.366317 | −0.183158 | − | 0.983083i | \(-0.558632\pi\) | ||||
−0.183158 | + | 0.983083i | \(0.558632\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.6724 | 1.20127 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.75386 | 0.347808 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.295298 | −0.0132193 | −0.00660967 | − | 0.999978i | \(-0.502104\pi\) | ||||
−0.00660967 | + | 0.999978i | \(0.502104\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27.1912 | 1.21481 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.6016 | −0.873993 | −0.436996 | − | 0.899463i | \(-0.643958\pi\) | ||||
−0.436996 | + | 0.899463i | \(0.643958\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −51.5144 | −2.28783 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.79383 | −0.0795102 | −0.0397551 | − | 0.999209i | \(-0.512658\pi\) | ||||
−0.0397551 | + | 0.999209i | \(0.512658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.4908 | 0.552562 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.49084 | 0.198275 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.08287 | −0.0476247 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.23407 | −0.361436 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.61850 | −0.114719 | −0.0573593 | − | 0.998354i | \(-0.518268\pi\) | ||||
−0.0573593 | + | 0.998354i | \(0.518268\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.9956 | −0.655713 | −0.327857 | − | 0.944728i | \(-0.606326\pi\) | ||||
−0.327857 | + | 0.944728i | \(0.606326\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.4340 | 1.28216 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.2234 | 1.79232 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.7755 | −0.901580 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.9571 | −0.647864 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.5693 | 1.40547 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.55102 | −0.239099 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.40608 | 0.146439 | 0.0732194 | − | 0.997316i | \(-0.476673\pi\) | ||||
0.0732194 | + | 0.997316i | \(0.476673\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −40.2341 | −1.72661 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.74760 | −0.202993 | −0.101496 | − | 0.994836i | \(-0.532363\pi\) | ||||
−0.101496 | + | 0.994836i | \(0.532363\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −50.2620 | −2.14513 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.35548 | 0.313354 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.57227 | 0.407054 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.0462 | 1.82393 | 0.911964 | − | 0.410271i | \(-0.134566\pi\) | ||||
0.911964 | + | 0.410271i | \(0.134566\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.6218 | −1.63353 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.65847 | 0.365561 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.0096 | −0.716869 | −0.358434 | − | 0.933555i | \(-0.616689\pi\) | ||||
−0.358434 | + | 0.933555i | \(0.616689\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.12473 | −0.0472343 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.7572 | −0.828264 | −0.414132 | − | 0.910217i | \(-0.635915\pi\) | ||||
−0.414132 | + | 0.910217i | \(0.635915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.3973 | 0.476964 | 0.238482 | − | 0.971147i | \(-0.423350\pi\) | ||||
0.238482 | + | 0.971147i | \(0.423350\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 36.5587 | 1.52726 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.3372 | −0.763386 | −0.381693 | − | 0.924289i | \(-0.624659\pi\) | ||||
−0.381693 | + | 0.924289i | \(0.624659\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.01832 | −0.291672 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.206167 | 0.00855327 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.05249 | 0.0850053 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.9475 | 0.493127 | 0.246563 | − | 0.969127i | \(-0.420699\pi\) | ||||
0.246563 | + | 0.969127i | \(0.420699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.11704 | 0.334457 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 54.9850 | 2.26178 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.3911 | −1.00162 | −0.500811 | − | 0.865557i | \(-0.666965\pi\) | ||||
−0.500811 | + | 0.865557i | \(0.666965\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −56.0943 | −2.29579 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.0708 | 0.860930 | 0.430465 | − | 0.902607i | \(-0.358350\pi\) | ||||
0.430465 | + | 0.902607i | \(0.358350\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.3878 | 1.32112 | 0.660562 | − | 0.750771i | \(-0.270318\pi\) | ||||
0.660562 | + | 0.750771i | \(0.270318\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.77551 | −0.194474 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.0183 | −0.771930 | −0.385965 | − | 0.922513i | \(-0.626131\pi\) | ||||
−0.385965 | + | 0.922513i | \(0.626131\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.4692 | 0.626843 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.04623 | −0.285060 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.5756 | −0.952210 | −0.476105 | − | 0.879389i | \(-0.657952\pi\) | ||||
−0.476105 | + | 0.879389i | \(0.657952\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.2707 | −1.05762 | −0.528810 | − | 0.848740i | \(-0.677361\pi\) | ||||
−0.528810 | + | 0.848740i | \(0.677361\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.4985 | −0.462165 | −0.231083 | − | 0.972934i | \(-0.574227\pi\) | ||||
−0.231083 | + | 0.972934i | \(0.574227\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −35.9894 | −1.44420 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.295298 | 0.0118309 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.38776 | 0.0953578 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.72928 | −0.0689510 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.8130 | 1.82379 | 0.911893 | − | 0.410427i | \(-0.134620\pi\) | ||||
0.911893 | + | 0.410427i | \(0.134620\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 49.8236 | 1.98031 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −36.1204 | −1.43114 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 47.1020 | 1.86333 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.36943 | 0.0540894 | 0.0270447 | − | 0.999634i | \(-0.491390\pi\) | ||||
0.0270447 | + | 0.999634i | \(0.491390\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.7389 | 0.975606 | 0.487803 | − | 0.872954i | \(-0.337799\pi\) | ||||
0.487803 | + | 0.872954i | \(0.337799\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.82611 | 0.268362 | 0.134181 | − | 0.990957i | \(-0.457160\pi\) | ||||
0.134181 | + | 0.990957i | \(0.457160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.88296 | −0.152420 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.0708 | 0.669058 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.91713 | 0.270688 | 0.135344 | − | 0.990799i | \(-0.456786\pi\) | ||||
0.135344 | + | 0.990799i | \(0.456786\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 75.8776 | 2.96027 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.44461 | −0.367910 | −0.183955 | − | 0.982935i | \(-0.558890\pi\) | ||||
−0.183955 | + | 0.982935i | \(0.558890\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.1955 | −0.863306 | −0.431653 | − | 0.902040i | \(-0.642070\pi\) | ||||
−0.431653 | + | 0.902040i | \(0.642070\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 56.3405 | 2.18808 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −58.9465 | −2.28242 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −37.3449 | −1.44384 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.39401 | −0.362652 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2986 | 0.474077 | 0.237039 | − | 0.971500i | \(-0.423823\pi\) | ||||
0.237039 | + | 0.971500i | \(0.423823\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.9527 | −1.38178 | −0.690888 | − | 0.722962i | \(-0.742780\pi\) | ||||
−0.690888 | + | 0.722962i | \(0.742780\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.47689 | −0.248560 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.5616 | 1.43937 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.00958 | 0.344742 | 0.172371 | − | 0.985032i | \(-0.444857\pi\) | ||||
0.172371 | + | 0.985032i | \(0.444857\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −37.5231 | −1.43160 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.3555 | 0.508803 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.11078 | 0.346590 | 0.173295 | − | 0.984870i | \(-0.444559\pi\) | ||||
0.173295 | + | 0.984870i | \(0.444559\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.04623 | 0.115717 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.64015 | 0.365147 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −70.5606 | −2.66885 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.7476 | −0.557009 | −0.278505 | − | 0.960435i | \(-0.589839\pi\) | ||||
−0.278505 | + | 0.960435i | \(0.589839\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.476886 | −0.0179861 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.5015 | 0.470166 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.63389 | −0.324253 | −0.162126 | − | 0.986770i | \(-0.551835\pi\) | ||||
−0.162126 | + | 0.986770i | \(0.551835\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 58.1483 | 2.18073 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −65.0496 | −2.43613 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −31.2909 | −1.16858 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.2759 | 1.42745 | 0.713726 | − | 0.700425i | \(-0.247006\pi\) | ||||
0.713726 | + | 0.700425i | \(0.247006\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.34153 | 0.273413 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.45856 | 0.128625 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1893 | 1.15675 | 0.578373 | − | 0.815772i | \(-0.303688\pi\) | ||||
0.578373 | + | 0.815772i | \(0.303688\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −44.0375 | −1.63102 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.8925 | 0.920684 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.9634 | −0.515748 | −0.257874 | − | 0.966179i | \(-0.583022\pi\) | ||||
−0.257874 | + | 0.966179i | \(0.583022\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.892548 | −0.0328774 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.02165 | −0.331867 | −0.165933 | − | 0.986137i | \(-0.553064\pi\) | ||||
−0.165933 | + | 0.986137i | \(0.553064\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.5371 | 0.570768 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.0342 | 0.551550 | 0.275775 | − | 0.961222i | \(-0.411066\pi\) | ||||
0.275775 | + | 0.961222i | \(0.411066\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.25240 | 0.0458228 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.26302 | −0.119228 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.6681 | −1.08260 | −0.541301 | − | 0.840829i | \(-0.682068\pi\) | ||||
−0.541301 | + | 0.840829i | \(0.682068\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.2557 | 1.06614 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.5819 | 0.384604 | 0.192302 | − | 0.981336i | \(-0.438405\pi\) | ||||
0.192302 | + | 0.981336i | \(0.438405\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.1354 | −0.694570 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.979789 | −0.0355173 | −0.0177587 | − | 0.999842i | \(-0.505653\pi\) | ||||
−0.0177587 | + | 0.999842i | \(0.505653\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.2201 | −0.369993 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.2663 | −0.912315 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.1772 | 1.55701 | 0.778505 | − | 0.627638i | \(-0.215978\pi\) | ||||
0.778505 | + | 0.627638i | \(0.215978\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.424399 | 0.0152844 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.5250 | 1.34968 | 0.674840 | − | 0.737964i | \(-0.264213\pi\) | ||||
0.674840 | + | 0.737964i | \(0.264213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.00293 | −0.0359799 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.65847 | 0.0952497 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.80342 | 0.315011 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.0323 | 1.18048 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.5833 | −0.805008 | −0.402504 | − | 0.915418i | \(-0.631860\pi\) | ||||
−0.402504 | + | 0.915418i | \(0.631860\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.39401 | 0.0496282 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.86171 | −0.279530 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −61.1266 | −2.17067 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.9806 | 1.27450 | 0.637250 | − | 0.770657i | \(-0.280072\pi\) | ||||
0.637250 | + | 0.770657i | \(0.280072\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.54144 | 0.160664 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.79383 | 0.0633820 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.1816 | 0.500457 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.65222 | 0.339774 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.955660 | −0.0335992 | −0.0167996 | − | 0.999859i | \(-0.505348\pi\) | ||||
−0.0167996 | + | 0.999859i | \(0.505348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.53707 | 0.264662 | 0.132331 | − | 0.991206i | \(-0.457754\pi\) | ||||
0.132331 | + | 0.991206i | \(0.457754\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.1127 | 0.530024 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.86464 | 0.240163 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 19.8217 | 0.692628 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.3082 | 0.464460 | 0.232230 | − | 0.972661i | \(-0.425398\pi\) | ||||
0.232230 | + | 0.972661i | \(0.425398\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.4050 | −0.850706 | −0.425353 | − | 0.905028i | \(-0.639850\pi\) | ||||
−0.425353 | + | 0.905028i | \(0.639850\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.6874 | 0.406411 | 0.203206 | − | 0.979136i | \(-0.434864\pi\) | ||||
0.203206 | + | 0.979136i | \(0.434864\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.6541 | 0.891004 | 0.445502 | − | 0.895281i | \(-0.353025\pi\) | ||||
0.445502 | + | 0.895281i | \(0.353025\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.7726 | −1.24094 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.2803 | 0.806615 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.4523 | 1.25998 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.91713 | 0.100710 | 0.0503552 | − | 0.998731i | \(-0.483965\pi\) | ||||
0.0503552 | + | 0.998731i | \(0.483965\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.1031 | 0.865624 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.424399 | −0.0146171 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.80779 | −0.268279 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −50.3544 | −1.72816 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.82174 | 0.131008 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.24281 | −0.213750 | −0.106875 | − | 0.994272i | \(-0.534084\pi\) | ||||
−0.106875 | + | 0.994272i | \(0.534084\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.2158 | −0.793035 | −0.396517 | − | 0.918027i | \(-0.629781\pi\) | ||||
−0.396517 | + | 0.918027i | \(0.629781\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.13536 | 0.243455 | 0.121728 | − | 0.992564i | \(-0.461157\pi\) | ||||
0.121728 | + | 0.992564i | \(0.461157\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.59099 | 0.190541 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.31362 | 0.248959 | 0.124479 | − | 0.992222i | \(-0.460274\pi\) | ||||
0.124479 | + | 0.992222i | \(0.460274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.6339 | 0.361146 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.8680 | 0.368671 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.80779 | −0.196789 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.3449 | −1.33162 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.0173 | −0.743471 | −0.371735 | − | 0.928339i | \(-0.621237\pi\) | ||||
−0.371735 | + | 0.928339i | \(0.621237\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.62953 | −0.189879 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.7572 | 0.396110 | 0.198055 | − | 0.980191i | \(-0.436538\pi\) | ||||
0.198055 | + | 0.980191i | \(0.436538\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.6560 | −1.87297 | −0.936487 | − | 0.350703i | \(-0.885943\pi\) | ||||
−0.936487 | + | 0.350703i | \(0.885943\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.41566 | 0.215417 | 0.107708 | − | 0.994183i | \(-0.465649\pi\) | ||||
0.107708 | + | 0.994183i | \(0.465649\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.9325 | −0.433743 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.27698 | −0.0427803 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.25240 | 0.0419098 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −124.513 | −4.15738 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 59.7047 | 1.99126 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.60788 | −0.286770 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.4369 | 0.480430 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 57.1160 | 1.89651 | 0.948253 | − | 0.317516i | \(-0.102849\pi\) | ||||
0.948253 | + | 0.317516i | \(0.102849\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 75.9421 | 2.51884 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.6339 | 0.882420 | 0.441210 | − | 0.897404i | \(-0.354549\pi\) | ||||
0.441210 | + | 0.897404i | \(0.354549\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.234074 | 0.00774672 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.412335 | −0.0136165 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.63246 | −0.218785 | −0.109392 | − | 0.993999i | \(-0.534890\pi\) | ||||
−0.109392 | + | 0.993999i | \(0.534890\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 45.6801 | 1.50521 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 57.2836 | 1.88551 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 44.5972 | 1.46477 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.0173 | −1.64101 | −0.820507 | − | 0.571637i | \(-0.806309\pi\) | ||||
−0.820507 | + | 0.571637i | \(0.806309\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.42003 | 0.210408 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −59.2976 | −1.94132 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.8882 | −1.30309 | −0.651545 | − | 0.758610i | \(-0.725879\pi\) | ||||
−0.651545 | + | 0.758610i | \(0.725879\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.09683 | 0.101061 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.59829 | −0.182499 | −0.0912495 | − | 0.995828i | \(-0.529086\pi\) | ||||
−0.0912495 | + | 0.995828i | \(0.529086\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.3049 | −0.693782 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.7110 | −0.413051 | −0.206525 | − | 0.978441i | \(-0.566216\pi\) | ||||
−0.206525 | + | 0.978441i | \(0.566216\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 92.2793 | 2.99551 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 82.5379 | 2.67648 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −57.0129 | −1.84683 | −0.923415 | − | 0.383804i | \(-0.874614\pi\) | ||||
−0.923415 | + | 0.383804i | \(0.874614\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.5631 | 0.567734 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.19221 | 0.0707903 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.8863 | 1.12536 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.8217 | −0.638747 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.0183 | 1.06180 | 0.530899 | − | 0.847435i | \(-0.321854\pi\) | ||||
0.530899 | + | 0.847435i | \(0.321854\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.0140 | −0.321695 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.04623 | 0.0977581 | 0.0488791 | − | 0.998805i | \(-0.484435\pi\) | ||||
0.0488791 | + | 0.998805i | \(0.484435\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.73221 | −0.0875907 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.4465 | 0.430192 | 0.215096 | − | 0.976593i | \(-0.430994\pi\) | ||||
0.215096 | + | 0.976593i | \(0.430994\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.335269 | 0.0107152 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −62.0837 | −1.98218 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.0646 | 0.703750 | 0.351875 | − | 0.936047i | \(-0.385544\pi\) | ||||
0.351875 | + | 0.936047i | \(0.385544\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.63389 | 0.0838378 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −55.0129 | −1.74931 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.9946 | −1.65166 | −0.825831 | − | 0.563917i | \(-0.809294\pi\) | ||||
−0.825831 | + | 0.563917i | \(0.809294\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 89.2330 | 2.83172 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.7693 | −1.19616 | −0.598082 | − | 0.801435i | \(-0.704070\pi\) | ||||
−0.598082 | + | 0.801435i | \(0.704070\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.14162 | −0.0677578 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7600.2.a.bi.1.1 | 3 | ||
4.3 | odd | 2 | 950.2.a.n.1.3 | 3 | |||
5.2 | odd | 4 | 1520.2.d.j.609.6 | 6 | |||
5.3 | odd | 4 | 1520.2.d.j.609.1 | 6 | |||
5.4 | even | 2 | 7600.2.a.cd.1.3 | 3 | |||
12.11 | even | 2 | 8550.2.a.ck.1.1 | 3 | |||
20.3 | even | 4 | 190.2.b.b.39.3 | ✓ | 6 | ||
20.7 | even | 4 | 190.2.b.b.39.4 | yes | 6 | ||
20.19 | odd | 2 | 950.2.a.i.1.1 | 3 | |||
60.23 | odd | 4 | 1710.2.d.d.1369.6 | 6 | |||
60.47 | odd | 4 | 1710.2.d.d.1369.3 | 6 | |||
60.59 | even | 2 | 8550.2.a.cl.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.b.b.39.3 | ✓ | 6 | 20.3 | even | 4 | ||
190.2.b.b.39.4 | yes | 6 | 20.7 | even | 4 | ||
950.2.a.i.1.1 | 3 | 20.19 | odd | 2 | |||
950.2.a.n.1.3 | 3 | 4.3 | odd | 2 | |||
1520.2.d.j.609.1 | 6 | 5.3 | odd | 4 | |||
1520.2.d.j.609.6 | 6 | 5.2 | odd | 4 | |||
1710.2.d.d.1369.3 | 6 | 60.47 | odd | 4 | |||
1710.2.d.d.1369.6 | 6 | 60.23 | odd | 4 | |||
7600.2.a.bi.1.1 | 3 | 1.1 | even | 1 | trivial | ||
7600.2.a.cd.1.3 | 3 | 5.4 | even | 2 | |||
8550.2.a.ck.1.1 | 3 | 12.11 | even | 2 | |||
8550.2.a.cl.1.3 | 3 | 60.59 | even | 2 |